Teaching Multiplicative Inverses

This chapter presents three cases on teaching multiplicative inverses using equal groups, array, and comparison models, each with two contrasting sub-cases illustrating different instructional approaches. In the TEPS approach (Cases 3a, 4a, and 5a), inverse word problems from the Common Core are used, and tape diagrams support the shift from concrete to abstract solutions. Deep questions are systematically posed to foster problem-posing, meaning-making, and comparison, engaging students at constructive and interactive ICAP levels. By contrast, the conventional approach (Cases 3b, 4b, and 5b) typically begins with abstract number sentences modeled with semi-concrete representations. Real-world contexts, if included, appear at the end as applications of computation skills. Teacher questions generally elicit answers rather than promote structural understanding, leaving quantitative reasoning underdeveloped and student engagement at passive or active ICAP levels. The chapter continues to employ a three-step process—think and prepare, read and annotate, stop and reflect—to engage readers. It examines instructional differences and their potential impact on student learning, highlighting the contrasts between the TEPS and conventional approaches within the ICAP framework.